1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mixer [17]
3 years ago
5

A farmer wants to fence a rectangular area of 72 square feet next to a river. Find the length and width of the rectangle which u

ses the least amount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river.
Mathematics
1 answer:
Arlecino [84]3 years ago
8 0

Answer:

  • 12 ft parallel to the river
  • 6 ft perpendicular to the river

Step-by-step explanation:

The least fence is used when half the total fence is parallel to the river. That is, the shape of the rectangle is twice as long as it is wide.

72 = W(2W)

36 = W²

6 = W . . . . . . the width perpendicular to the river

12 = 2W . . . .  the length parallel to the river

_____

<em>Development of this relation</em>

Let T represent the total length of the fence for some area A. Then if x is the length along the river, the width is y=(T-x)/2, and the area is ...

  A = xy = x(T -x)/2

Note that the equation for area is that of a parabola with zeros at x=0 and at x=T. That is, for some fence length T, the area will be a maximum at the vertex of this parabola. That vertex is located halfway between the zeros, at ...

 x = (0 +T)/2 = T/2

The corresponding area width (y) is ...

  y = (T -T/2)/2 = T/4

Equivalently, the fence length T will be a minimum for some area A when x=T/2 and y=T/4. This is the result we used above.

You might be interested in
Qual o nome do instrumento usado para medir os graus de um ângulo?
Aleks [24]
<span>English: What is the name of the instrument used to measure the degrees of an angle?

responder: 
transportador</span>
7 0
3 years ago
Please help :) Which expression is equal to 5 plus 4 times 2 minus 6?
nirvana33 [79]

Answer:

5 + 8 - 6

Step-by-step explanation:

or if you want a solved answer its 7.

6 0
2 years ago
Read 2 more answers
Can someone please do this for me, It would be amazing!<br><br>sorry that's all the points I have :(
Serggg [28]

If i was you i would look up every box in the word bank then find examples of each box and do the best I could.

-hope this helps!

7 0
3 years ago
PLEASE PLEASE HELP!!! Figure 1 is dilated to get figure 2. What is the scale factor? Figure 1 is the smaller figure and has a 6
Xelga [282]
The answer is 1.5

Hope this helps!!
6 0
3 years ago
The perimeter of another quilt had to be 34 feet because he only had that much binding. If he wanted it to be 8 feet long, what
Mila [183]
72ft
you do 8 times 2 is 16
34-16 is 18 then divide by 2 is 9
9 times 8 is 72
~JZ

7 0
3 years ago
Other questions:
  • Slope-10 pass through (2,-5)
    9·1 answer
  • Suppose that a is a nonzero constant for which the equation ax^2+20x+7=0 has only one solution. find this solution.
    15·1 answer
  • A stadium has 50 comma 00050,000 seats. Seats sell for ​$3030 in Section​ A, ​$2424 in Section​ B, and ​$1818 in Section C. The
    6·1 answer
  • A wire is tied from the top of one tower to the top of another. The angle of depression from the top
    8·1 answer
  • -7y+11y+9=-3 what does y equal
    15·1 answer
  • In the equation below, what is the first step? <br> 18- 3x =12
    5·1 answer
  • What is the ratio of 6/4 in simplest form??
    11·1 answer
  • Find the 60th term of the sequence below. 3, 7, 11, 15...​
    5·1 answer
  • 3. Convert this rate (80km/hr) to a rate measured in m/s​
    14·1 answer
  • PLEASE HELP ASAP:)!!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!